A conical pendulum is a mass on a string that traces a horizontal circle, with the string
Circular Motion - OCR A-Level Physics
- A conical pendulumA mass on a string that traces a horizontal circle, with the string sweeping out a cone shape. is a mass on a string that traces a horizontal circle, with the string sweeping out a cone shape.
- The vertical component of tension balances weight: $T\cos\theta$ = mg.
- The horizontal component of tension provides centripetal forceThe resultant force directed towards the centre of a circular path that causes an object to move in a circle. It is not a separate force but the net force providing circular motion.: $T\sin\theta$ = mv^2/r = $mr\omega$^2.
- Dividing these: $\tan\theta$ = \(v^{2}\)/(rg) = $r\omega$^2/g.
- The radius of the circle is r = $L\sin\theta$ where L is the string length.
- The periodThe time taken for one complete oscillation or wave cycle. Measured in seconds (s). is T = $2\pi\sqrt{L\cos\theta / g}$, which depends $on \theta$and L but not on mass.
Common Mistake
MEDIUM
Wrong: Setting tension equal to weight ($T = mg)$ for a conical pendulum.
Right: Only the vertical component of tension equals weight: T\cos\$\theta = mg. The full tension T$ is always greater than mg because it also has a horizontal component providing centripetal forceThe resultant force directed towards the centre of a circular path that causes an object to move in a circle. It is not a separate force but the net force providing circular motion..
Right: Only the vertical component of tension equals weight: T\cos\$\theta = mg. The full tension T$ is always greater than mg because it also has a horizontal component providing centripetal forceThe resultant force directed towards the centre of a circular path that causes an object to move in a circle. It is not a separate force but the net force providing circular motion..